天文、气象地理可视化adaptive annealed importance sampling for bayesian multimodal posterior exploration

1、Adaptive Annealed Importance Sampling for Bayesian Multimodal Posterior ExplorationA Bayesian approach to search extra-solar planets 1 2 String theory 3 4 5 6 7 A screenshot of a JPLs website 8 9 Space and Ground Missions : Kepler Launched:March 7, 2009Location:SpaceOperated by:NASA 10 Space and Gro

2、und Missions : Spitzer Space Telescope Launched: August 25, 2003Location: SpaceOperated by: NASA 11 Space and Ground Missions : Hubble Space TelescopeLaunched: April 24, 1990Location: SpaceOperated by: NASA 12 Space and Ground Missions : CoRoTLaunched: December 27, 2006Location: SpaceOperated by: CN

3、ES/ESA 13 Large Binocular Telescope Interferometer (LBTI)First light: December 7, 2010Location: Mt. Graham, ArizonaOperated by: University of Arizona 14 15 Radial Velocity Technique 16 Bayesian Methodology 17 “Methods can be abused and that is true with any approach, including Bayesian but it offers

4、 a more coherent, philosophical way in which to look at the world ”Bayesian Statistics General Philosophy 18 In Bayesian statistics, interpretation of probability extended to degree of belief (subjective probability). Use this for hypotheses:posterior probability, i.e., after seeing the dataprior pr

5、obability, i.e.,before seeing the dataprobability of the data assuming hypothesis H (the likelihood)normalization involves sum over all possible hypothesesBayesian inference embodies Occam razor This figure gives the basic intuition for why complexmodels can turn out to be less probable. 19 Kepleria

6、n Radial Velocity Model 20 Multimodality in the likelihood slices 21 The candidate modelsNull-planet model 22 One-planet modelIn a p-planet modelMarginal likelihoods and Bayes factor 23 Computational TasksPosterior sampling 24 Model (marginal) likelihood computationImportance Sampling 25 Building a

7、Good Importance Sampler 26 27 Simulation case I 28 Simulation case II 29 Simulation case III 30 Simulation case IV 31 Simulation case IV 32 A real data case 33 A real data caseA real data caseA real data caseA real data caseA summarization on AAIS Abandon MCMC! (support parallelization) Use sequenti

8、al Monte Carlo to build importance sampler from q() Gives posterior samples and marginal likelihood Blind start Simultaneous parameter estimation, model selection and uncertainty qualification 38 See details inLiu, B., Adaptive Annealed Importance Sampling for Multi-modal Posterior Exploration and Model Selection with Application to Extrasolar Planet Detection, The Astrophysical Journal Supplement Series, vol.213, no.1, pp.14, 2014. (JCR一区, IF:14.14)Loredo, T.J., Berger, J.O., Chernoff, D.F., Clyde, M.A. and Liu, B., Bayesian Methods for Analysis and Ada